First thing you need to do is download the BYOND installer for Linux. Unzip the file and take a look at the readme files in there. Documentation is a bit sparse, but enough to get you going. Once installed (you should be able to install it within your local account, I believe), you just need to run DreamDaemon with the dmb file you want to host. It has some extra command-line options you may be interested in: either type DreamDaemon at the command line or look in the readmes for more information.

Not much to it, really. I'm hosting the multiplayer versions of ShapeShifter and Search Engine Wars from my own PC using the FreeBSD version (same thing, more or less).